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A374753
Decimal expansion of the volume of a regular dodecahedron having unit inradius.
6
5, 5, 5, 0, 2, 9, 1, 0, 2, 8, 5, 1, 5, 5, 1, 0, 2, 6, 9, 0, 7, 0, 4, 3, 2, 1, 1, 3, 6, 6, 1, 8, 3, 9, 2, 4, 0, 7, 3, 7, 5, 9, 8, 2, 1, 2, 8, 8, 2, 4, 9, 8, 8, 6, 7, 1, 1, 1, 7, 5, 3, 8, 6, 3, 5, 3, 8, 8, 3, 6, 7, 0, 7, 3, 3, 3, 2, 4, 5, 2, 3, 6, 4, 8, 2, 9, 3, 8, 8, 9
OFFSET
1,1
COMMENTS
The dodecahedral conjecture (proved in 1988 by Thomas C. Hales and Sean McLaughlin, see links) states that, in any packing of unit spheres in the Euclidean 3-space, every Voronoi cell has volume at least equal to this value.
LINKS
Thomas C. Hales and Sean McLaughlin, A proof of the dodecahedral conjecture, arXiv:math/9811079 [math.MG], 2008.
Thomas C. Hales and Sean McLaughlin, The Dodecaheral Conjecture, Journal of the American Mathematical Society, Vol. 23, No. 2, April 2010, pp. 299-344.
FORMULA
Equals (4/3)*Pi/A374772 = 10*A019699/A374772.
Equals 10*sqrt(130 - 58*sqrt(5)).
Equals A374755/3.
EXAMPLE
5.55029102851551026907043211366183924073759821288...
MATHEMATICA
First[RealDigits[10*Sqrt[130 - 58*Sqrt[5]], 10, 100]]
CROSSREFS
Cf. A019699, A374755 (strong dodecahedral conjecture), A374772 (density).
Sequence in context: A344235 A019253 A019173 * A230192 A172359 A093796
KEYWORD
nonn,cons
AUTHOR
Paolo Xausa, Jul 19 2024
STATUS
approved